Gaussian process emulators for spatial individual-level models of infectious disease

Ensemble learning methods of inference for spatially stratified infectious disease systems

Individual level models are a class of mechanistic models that are widely used to infer infectious disease transmission dynamics. These models incorporate individual level covariate information accounting for population heterogeneity and are generally fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. However, Bayesian MCMC methods of inference are computationally expensive for large data sets. This issue becomes more severe when applied to infectious disease data collected from spatially heterogeneous populations, as the number of covariates increases. In addition, summary statistics over the global population may not capture the true spatio-temporal dynamics of disease transmission. In this study we propose to use ensemble learning methods to predict epidemic generating models instead of time consuming Bayesian MCMC method. We apply these methods to infer disease transmission dynamics over spatially clustered populations, considering the clusters as natural strata instead of a global population. We compare the performance of two tree-based ensemble learning techniques: random forest and gradient boosting. These methods are applied to the 2001 foot-and-mouth disease epidemic in the U.K. and evaluated using simulated data from a clustered population. It is shown that the spatially clustered data can help to predict epidemic generating models more accurately than the global data.

Variable screening methods in spatial infectious disease transmission models

Data-driven mathematical modelling can enrich our understanding of infectious disease spread enormously. Individual-level models of infectious disease transmission allow the incorporation of different individual-level covariates, such as spatial location, vaccination status, etc. This study aims to explore and develop methods for fitting such models when we have many potential covariates to include in the model. The aim is to enhance the performance and interpretability of models and ease the computational burden of fitting these models to data. We have applied and compared multiple variable selection methods in the context of spatial epidemic data. These include a Bayesian two-stage least absolute shrinkage and selection operator (Lasso), forward and backward stepwise selection based on the Akaike information criterion (AIC), spike-and-slab priors, and random variable selection (boosting) methods. We discuss and compare the performance of these methods via simulated datasets and UK 2001 foot-and-mouth disease data. While comparing the variable selection methods all performed consistently well except the two-stage Lasso. We conclude that the spike-and-slab prior method is to be recommended, consistently resulting in high accuracy and short computational time.

An individual level infectious disease model in the presence of uncertainty from multiple, imperfect diagnostic tests

Bayesian compartmental infectious disease models yield important inference on disease transmission by appropriately accounting for the dynamics and uncertainty of infection processes. In addition to estimating transition probabilities and reproductive numbers, these statistical models allow researchers to assess the probability of disease risk and quantify the effectiveness of interventions. These infectious disease models rely on data collected from all individuals classified as positive based on various diagnostic tests. In infectious disease testing, however, such procedures produce both false-positives and false-negatives at varying rates depending on the sensitivity and specificity of the diagnostic tests being used. We propose a novel Bayesian spatio-temporal infectious disease modeling framework that accounts for the additional uncertainty in the diagnostic testing and classification process that provides estimates of the important transmission dynamics of interest to researchers. The method is applied to data on the 2006 mumps epidemic in Iowa, in which over 6,000 suspected mumps cases were tested using a buccal or oral swab specimen, a urine specimen, and/or a blood specimen. Although all procedures are believed to have high specificities, the sensitivities can be low and vary depending on the timing of the test as well as the vaccination status of the individual being tested.

Spatiotemporal high-resolution prediction and mapping: methodology and application to dengue disease

Dengue disease has become a major public health problem. Accurate and precise identification, prediction and mapping of high-risk areas are crucial elements of an effective and efficient early warning system in countering the spread of dengue disease. In this paper, we present the fusion area-cell spatiotemporal generalized geoadditive-Gaussian Markov random field (FGG-GMRF) framework for joint estimation of an area-cell model, involving temporally varying coefficients, spatially and temporally structured and unstructured random effects, and spatiotemporal interaction of the random effects. The spatiotemporal Gaussian field is applied to determine the unobserved relative risk at cell level. It is transformed to a Gaussian Markov random field using the finite element method and the linear stochastic partial differential equation approach to solve the "big n" problem. Sub-area relative risk estimates are obtained as block averages of the cell outcomes within each sub-area boundary. The FGG-GMRF model is estimated by applying Bayesian Integrated Nested Laplace Approximation. In the application to Bandung city, Indonesia, we combine low-resolution area level (district) spatiotemporal data on population at risk and incidence and high-resolution cell level data on weather variables to obtain predictions of relative risk at subdistrict level. The predicted dengue relative risk at subdistrict level suggests significant fine-scale heterogeneities which are not apparent when examining the area level. The relative risk varies considerably across subdistricts and time, with the latter showing an increase in the period January-July and a decrease in the period August-December.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s10109-021-00368-0.

Wearable Edge AI Applications for Ecological Environments

Ecological environments research helps to assess the impacts on forests and managing forests. The usage of novel software and hardware technologies enforces the solution of tasks related to this problem. In addition, the lack of connectivity for large data throughput raises the demand for edge-computing-based solutions towards this goal. Therefore, in this work, we evaluate the opportunity of using a Wearable edge AI concept in a forest environment. For this matter, we propose a new approach to the hardware/software co-design process. We also address the possibility of creating wearable edge AI, where the wireless personal and body area networks are platforms for building applications using edge AI. Finally, we evaluate a case study to test the possibility of performing an edge AI task in a wearable-based environment. Thus, in this work, we evaluate the system to achieve the desired task, the hardware resource and performance, and the network latency associated with each part of the process. Through this work, we validated both the design pattern review and case study. In the case study, the developed algorithms could classify diseased leaves with a circa 90% accuracy with the proposed technique in the field. This results can be reviewed in the laboratory with more modern models that reached up to 96% global accuracy. The system could also perform the desired tasks with a quality factor of 0.95, considering the usage of three devices. Finally, it detected a disease epicenter with an offset of circa 0.5 m in a 6 m × 6 m × 12 m space. These results enforce the usage of the proposed methods in the targeted environment and the proposed changes in the co-design pattern.

Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19

We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin S = 1/2 Ising-like model and a (logistic) Fermi-Dirac-like function to describe the spread of Covid-19. Our analysis show that: (i) in many cases the epidemic curve can be described by a Gaussian-type function; (ii) the temporal evolution of the accumulative number of infections and fatalities follow a logistic function; (iii) the key role played by the quarantine to block the spread of Covid-19 in terms of an interacting parameter between people. In the frame of elementary percolation theory, we show that: (i) the percolation probability can be associated with the probability of a person being infected with Covid-19; (ii) the concepts of blocked and non-blocked connections can be associated, respectively, with a person respecting or not the social distancing. Yet, we make a connection between epidemiological concepts and well-established concepts in condensed matter Physics.

Spatial modeling of individual-level infectious disease transmission: Tuberculosis data in Manitoba, Canada

Geographically dependent individual level models (GD-ILMs) are a class of statistical models that can be used to study the spread of infectious disease through a population in discrete-time in which covariates can be measured both at individual and area levels. The typical ILMs to illustrate spatial data are based on the distance between susceptible and infectious individuals. A key feature of GD-ILMs is that they take into account the spatial location of the individuals in addition to the distance between susceptible and infectious individuals. As a motivation of this article, we consider tuberculosis (TB) data which is an infectious disease which can be transmitted through individuals. It is also known that certain areas/demographics/communities have higher prevalent of TB (see Section 4 for more details). It is also of interest of policy makers to identify those areas with higher infectivity rate of TB for possible preventions. Therefore, we need to analyze this data properly to address those concerns. In this article, the expectation conditional maximization algorithm is proposed for estimating the parameters of GD-ILMs to be able to predict the areas with the highest average infectivity rates of TB. We also evaluate the performance of our proposed approach through some simulations. Our simulation results indicate that the proposed method provides reliable estimates of parameters which confirms accuracy of the infectivity rates.

Contact network uncertainty in individual level models of infectious disease transmission

Infectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. This contact network can be spatial in nature, with connections between individuals closer in space being more likely. However, contact network data are often unobserved. Here, we consider the fit of an individual level model containing a spatially-based contact network that is either entirely, or partially, unobserved within a Bayesian framework, using data augmented Markov chain Monte Carlo (MCMC). We also incorporate the uncertainty about event history in the disease data. We also examine the performance of the data augmented MCMC analysis in the presence or absence of contact network observational models based upon either knowledge about the degree distribution or the total number of connections in the network. We find that the latter tend to provide better estimates of the model parameters and the underlying contact network.

Local rabies transmission and regional spatial coupling in European foxes

Infectious diseases are often transmitted through local interactions. Yet, both surveillance and control measures are implemented within administrative units. Capturing local transmission processes and spatial coupling between regions from aggregate level data is therefore a technical challenge that can shed light on both theoretical questions and practical decisions. Fox rabies has been eliminated from much of Europe through oral rabies vaccination (ORV) programmes. The European Union (EU) co-finances ORV to maintain rabies freedom in EU member and border states via a cordon sanitaire. Models to capture local transmission dynamics and spatial coupling have immediate application to the planning of these ORV campaigns and to other parts of the world considering oral vaccination. We fitted a hierarchical Bayesian state-space model to data on three decades of fox rabies cases and ORV campaigns from Eastern Germany. Specifically, we find that (i) combining regional spatial coupling and heterogeneous local transmission allows us to capture regional rabies dynamics; (ii) incursions from other regions account for less than 1% of cases, but allow for re-emergence of disease; (iii) herd immunity achieved through bi-annual vaccination campaigns is short-lived due to population turnover. Together, these findings highlight the need for regular and sustained vaccination efforts and our modelling approach can be used to provide strategic guidance for ORV delivery. Moreover, we show that biological understanding can be gained from inference from partially observed data on wildlife disease.

Geographically dependent individual-level models for infectious diseases transmission

Infectious disease models can be of great use for understanding the underlying mechanisms that influence the spread of diseases and predicting future disease progression. Modeling has been increasingly used to evaluate the potential impact of different control measures and to guide public health policy decisions. In recent years, there has been rapid progress in developing spatio-temporal modeling of infectious diseases and an example of such recent developments is the discrete-time individual-level models (ILMs). These models are well developed and provide a common framework for modeling many disease systems; however, they assume the probability of disease transmission between two individuals depends only on their spatial separation and not on their spatial locations. In cases where spatial location itself is important for understanding the spread of emerging infectious diseases and identifying their causes, it would be beneficial to incorporate the effect of spatial location in the model. In this study, we thus generalize the ILMs to a new class of geographically dependent ILMs, to allow for the evaluation of the effect of spatially varying risk factors (e.g., education, social deprivation, environmental), as well as unobserved spatial structure, upon the transmission of infectious disease. Specifically, we consider a conditional autoregressive (CAR) model to capture the effects of unobserved spatially structured latent covariates or measurement error. This results in flexible infectious disease models that can be used for formulating etiological hypotheses and identifying geographical regions of unusually high risk to formulate preventive action. The reliability of these models is investigated on a combination of simulated epidemic data and Alberta seasonal influenza outbreak data ($2009$). This new class of models is fitted to data within a Bayesian statistical framework using Markov chain Monte Carlo methods.

Incorporating Contact Network Uncertainty in Individual Level Models of Infectious Disease using Approximate Bayesian Computation

Infectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. However, such contact network data are often unobserved. Such missing data can be accounted for in a Bayesian data augmented framework using Markov chain Monte Carlo (MCMC). Unfortunately, fitting models in such a framework can be highly computationally intensive. We investigate the fitting of network-based infectious disease models with completely unknown contact networks using approximate Bayesian computation population Monte Carlo (ABC-PMC) methods. This is done in the context of both simulated data, and data from the UK 2001 foot-and-mouth disease epidemic. We show that ABC-PMC is able to obtain reasonable approximations of the underlying infectious disease model with huge savings in computation time when compared to a full Bayesian MCMC analysis.